Question

the digits 1, 2, 3, 4 are used to generate 256 different four digit numbers find the sum of all those 256 numbers

Answer 1

As each digit of four digit number (abcd) can take 4 options (1, 2, 3, 4) total there can be 4^4 numbers.
Obviously each digit (a, b, c, and d) will take the value of 1, 2, 3, 4 equal number of times, so each digit will take the value of 1, 2, 3, 4 - 444=43=64444=43=64 times: units digit will take the values of 1, 2, 3, 4 - 64 times and the same with tens, hundreds, thousands digits.
So the sum would be 64*(1+2+3+4)+64*10*(1+2+3+4)+64*100*(1+2+3+4)+64*1000*(1+2+3+4)=64*10*(1+10+100+1000)=711040.
Actually there is the direct formula for this kind of problems. Of course it's better to understand the concept, then to memorize the formula but in case someone is interested here it is:
1. Sum of all the numbers which can be formed by using the nn digits without repetition is: (n-1)!*(sum of the digits)*(111…..n times).
Hope it helps ...

Answer 2

Answer: 711040

Step-by-step explanation:

As each digit of four digit number (abcd) can take 4 options (1, 2, 3, 4) total there can be 4^4 numbers.

Obviously each digit (a, b, c, and d) will take the value of 1, 2, 3, 4 equal number of times, so each digit will take the value of 1, 2, 3, 4 - 444=43=64444=43=64 times: units digit will take the values of 1, 2, 3, 4 - 64 times and the same with tens, hundreds, thousands digits. the sum would be 64*(1+2+3+4)+64*10*(1+2+3+4)+64*100*(1+2+3+4)+64*1000*(1+2+3+4)=64*10*(1+10+100+1000)=711040.